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Can someone please summarize the exact difference between NP-Complete and NP-Hard problems in simple language? Wiki and my standard books aren't exactly helping.

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closed as too localized by Aaron Roth, Kaveh, Tsuyoshi Ito, Noam, Daniel Apon Oct 9 '10 at 17:38

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too elementary (defined very well on wiki and in any decent introduction to complexity book), voting to close. – Kaveh Oct 9 '10 at 17:20
To voters: when you vote to close as too elementary, please consider to use “too localized” instead of “off topic” as a reason. – Tsuyoshi Ito Oct 9 '10 at 17:30
@chronoz, I would highly recommend reading the site's FAQ if you have any questions about why this question was closed, especially this and this. – Daniel Apon Oct 9 '10 at 17:42

A NP-complete problem is an NP-hard problem which is in NP.

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Figured I'd slip in a quick comment, in case it helps the OP, before the question is closed for being too elementary: Monoid's answer is the correct definition. Some further, natural implications: Any problem harder than an NP-complete problem is NP-hard; NP-complete problems are NP-hard; any problem easier than an NP-complete problem is not NP-hard. – Daniel Apon Oct 9 '10 at 17:38